Express this product in scientific notation: $(5.00\times 10^{-1})\times (9.00\times 10^{5})$
Solution: Start by collecting like terms together. $= (5.00\times 9.00) \times (10^{-1}\times 10^{5})$ When multiplying exponents with the same base, add the powers together. $= 45.0 \times 10^{-1\,+\,5}$ $= 45.0 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $45.0$ is the same as $4.500 \times 10$ $ = {4.500 \times 10} \times 10^{4} $ $= 4.500\times 10^{5}$